and \((b_1,b_2,b_3)=(-24, 240, -504)\) , was discovered by Ramanujan in [1]} and it is mainly known
as Ramanujan's relations between Eisenstein series.
Ramanujan was a master of formal power series
and had a very limited access to the modern mathematics of his time.
In particular, he and many people in number theory didn't know that the differential equation (REF ) had already been studied by Halphen in his book [2]}, thirty years before S. Ramanujan.
The equalities of the coefficients of \(x^i\)  in
\(4(x-t_1)(x-t_2)(x-t_3)=4(x-a_1E_2)^3-a_2E_4(x-a_1E_2)-a_3E_6,\) 
